Recently, in the field of the mobile communication such as the automobile telephone and the pedestrian telephone, the code division multiple access (CDMA) transmission system has come into practical use. The principle of the CDMA transmission system will be summarized as follows.
A carrier signal in each symbol period of a certain length is subjected to Phase Shift Keying (PSK) according to information to be transmitted, to generate a primary modulated wave. In that case, if necessary, primary modulated waves are generated more than the number n of channels used for the code division multiple access.
The primary modulated wave is multiplied by.a spread code of a specified code length such as 32 or 64, repeating a plurality of times equal to the number of segments in each symbol period, to generate a spread signal. The length of this spread code sequence is equal to the so-called spread factor. Further, it is assumed that spread codes are provided by a Walsh function or the like, and orthogonal to one another. Further, in a single spread code in each symbol period, a period from the first code to the last code is called a segment. Each symbol period consists of a plurality of segments. In particular, a segment corresponding to a spread code is called “transmission basic segment” or simply “basic segment”. As referred to in describing the technique of despreading, a segment corresponding to a despread code is similarly called “basic segment” or simply “basic segment”.
For every transmission basic segment and reception basic segment, the leading edge point and the trailing edge point coincide respectively with the point in the leading edge of the first code and the point in the trailing edge of the last code of the spread code or despread code. Except for delay times such as a processing delay and a transmission delay in transmission and reception, the transmission basic segment and the reception basic segment coincide temporally with each other. In this sense, “transmission basic segment” and “reception basic segment” are generally called “basic segment”, and differentiated from “virtual segment”. Here, “virtual segment” is a new concept disclosed in the present invention for improving receiving performance. Further, “transmission segment” is used for specifying a segment used for despread starting from a non-coincident point of time.
Adding n spread codes required for multiple access simultaneously utilizing n channels and at least one spread code indicating phase compensation information and control information required for the communication system, the sum total obtained by adding at least (n+1) spread signals is transmitted.
On the other hand, on a receiving side, control information such as chip timing, symbol timing, symbol period, and segment period is detected from a received wave. Then, the received wave is multiplied by a despread code corresponding to the spread code used at the time of transmission, so that the sum total of the received segments for the period during which the despread code continuity is obtained, to determine the despread value. For each symbol, the despread signal is obtained from the despread values of a plurality of received segments existing within the symbol period, to demodulate the primary modulated wave from a despreading circuit and to detect information phase within the symbol period. The phase value detected in this way is called a detected phase value. In mobile communication, severe fading occurs frequently, so that a phase error is generated in the detected phase value, largely deviating from a correct phase value. Thus, in order to compensate a phase error, a known phase value such as zero is subjected to the primary modulation and then a pilot signal obtained by spreading with a specific spread code, which is transmitted at the same time with the primary modulation. When the pilot signal is received, it is possible to know the phase error from the previously-known phase value. Assuming that phase errors of the same value arise with respect to all the spread codes, and subtracting that phase error from the detected phase value to correct it, disturbance due to fading etc. can be suppressed.
Next, information corresponding to the detected phase value corrected is identified, thus accomplishing transmission of the information.
Such conventional technique of CDMA transmission system will be further described referring to the drawings. In the figures, the same or like numerals or symbols denote the same or like components.
FIG. 26 shows an outlined configuration of an ordinary CDMA transmitter. In FIG. 26, a known value used for a pilot signal is inputted through an input terminal 100 and information values are inputted through n information input terminals 101-10n, to corresponding phase modulation circuits (MOD) 110 and 111-11n, respectively. The number n of the inputted information values means the number of channels simultaneously utilized in multiple access.
According to the inputted information, the phase modulation circuits perform phase modulation of a carrier signal to generate (n+1) primary modulated waves corresponding to the signals received through the input terminals 100-10n, respectively.
Spreading circuits (SS) 120-12n obtain the products of corresponding primary modulated waves and the spread codes applied from spread code generating circuits (CG) 130-130n, synchronously with the correspondence of the spread codes with the period of time (chip period), and output the obtained products as the spread codes, respectively. Here, the spread codes generated by the spread code generating circuits (CG) 130-13n are orthogonal to one another. Further, the spread code generating circuits (CG) are synchronous with one another, and generate spread codes corresponding to each line of a Walsh function and having the code length N more than or equal to (n+1), within one symbol period and repeating a plurality of times corresponding to the number of the segments, respectively.
Then, (n+1) spread codes and various control signals are summed in a summing circuit (SUM) 140. Output of the summing circuit (SUM) 140 is limited in its frequency band width by a bandlimiting circuit (BPF) 141, and if necessary, subjected to frequency conversion and power amplification in a transmitting circuit (TX) 142, prior to transmission.
Now, operation of the phase modulation circuits (MOD) 110-11n in the above-mentioned FIG. 26 will be described in detail in the following. Namely, in each of the phase modulation circuits (MOD) 110-11n, the carrier signal is divided into periods of a prescribed period T as shown by the primary modulated wave and symbol structure of FIG. 27. Phase of the carrier signal is modulated so that a phase of each period corresponds one-to-one to a symbol value 00, 01, 10, or 11 transmitted in one period, in accordance with the bit arrangement of QPSK shown in FIG. 28 or the bit arrangement of π/4-shifted QPSK shown in FIG. 29, to generate a primary modulated wave.
Here, the primary modulated wave generally refers to phase-modulated signals generated by QPSK, offset QPSK, differential QPSK, π/4-shifted differential QPSK, or the like. Further, when, as described above, QPSK is used for generating a primary modulated wave, it is assumed that a phase of a QPSK wave takes four kinds of values 0, 90, 180 and 270 degrees (or, 0, ±90 and ±180 degrees). When π/4-shifted QPSK is used, phase information of a QPSK wave takes four kinds of values 45, 135, 225 and 315 degrees (or, ±45 and ±135 degrees). Phase values are residues of 360 degrees, and phases of QPSK waves are set to divide the total phase space into the maximum parts. For example, when it is assumed that the reference phase is 0 degree in QPSK or 45 degrees in π/4-shifted QPSK, all the phases are spaced from each other at intervals of 90 degrees. By making four kinds of phases of primary waves correspond to the states 00, 01, 10 and 11, a transmission bit series can be made to correspond to a series of dibits each being a combination of two bits. Thus, each symbol can transmit two bits.
As shown in the figures, the symbols are set as 00, 01, 11, and 10 counterclockwise in order that a Hamming distance corresponding to adjacent phases becomes 1 and a Hamming distance corresponding to non-adjacent phases becomes 2. Here, the Hamming distance means the number of different bit values between states. For example, distance (00, 01), distance (01, 11), distance (11, 10) and distance (10, 00) are all 1, while distance (00, 11) and distance (10, 01) are each 2.
Such phase-to-state mapping is called Gray coding, and used for suppressing probability of a transmitted information error due to disturbances during propagation to a lower level. Logically, even when the received phase is shifted more than 45 degrees from the transmitted phase due to a disturbance and taken erroneously as an adjacent state, one bit out of the two is saved since the distance from the adjacent states is always set at 1.
As a matter of course, when phase error of 135 degrees or more arises, all the two bits become errors. In that case, however, any state assignment leads to all bit error, which can not be saved by Gray coding. Thus, it is impossible to save such an error without introducing an error correcting code or the like.
On the other hand, the symbol period T is a quantity defined by the reciprocal of the symbol rate. For example, when the symbol rate is 32 k symbol/sec. (hereinafter, symbol/sec will be expressed as sps), T becomes T=31.25 μseconds. When, the symbol rate is 32 ksps, the transmission speed of QPSK becomes 64 k bit/sec. (hereinafter, bit/sec. will be expressed as bps).
Next, operation of the spreading circuits (SS) 120-12n of FIG. 26 will be described in more detail.
Now, as shown in FIG. 30, each symbol period of a primary modulated wave is divided into four segment intervals, Segment 0 through Segment 3, each being the same period of time. Here, is given a description of the case of four segments per symbol. However, the other cases are similar and can be understood by analogy. Accordingly, their description will be omitted. Further, as shown in FIG. 31, each segment interval is divided into chip intervals, the number of which is equal to the number of codes in the spread code sequence. Further, it is assumed that a chip value is given by the product of a primary modulated wave and a spread code value in each chip interval. Since a primary modulated wave is a function of time, time resolution of a chip value is the chip period τ. However, since CDMA performs spreading operation and later-described despreading operation on a receiving side, time resolution of transmitted information is the segment period τN. Here, N is the code length.
The waveform of the spread signal shown in FIG. 31 shows a case in which the first code of a Walsh function having code length of 32 is used as the spread code.
Generally, a Walsh function is given by the following recurrence formula.                               W                      2            ⁢            N                          =                                                                                        W                  N                                                                              W                  N                                                                                                      W                  N                                                                                                  W                    N                                    _                                                                                                  (        1        )            where W2N is a square matrix of 2N×2N,
WN is a square matrix of N×N, and
{overscore (WN)} is a square matrix of N×N whose elements are complements of the elements of WN.
For example, W2 whose element is square matrix of 1×1, i.e. a scalar, is given as follows.                               W          2                =                                                                      0                                            0                                                                    0                                            1                                                                                  (        2        )            
A row of such Walsh function W2N is used as a code sequence. Here, however, 0 of the Walsh function is made to correspond to “−1” and 1 of the Walsh function to “1”. Then, when, for example, the i-th row is synchronized with chip times, zeroth to 31st colums, within a segment, a code sequence called an i-th Walsh code sequence is obtained. Here, 0≦i≦N−1, and N is the rank of the Walsh function.
Although it is not necessary to use a Walsh code as a spread code, it is necessary that the code sequences are orthogonal to each other. Here, when the inner product of codes is zero, then it is said that those codes are orthogonal. Further, a Walsh code having a code length of 32 will be described. However, description of the other cases such as the code length of 64 will be omitted, since they are similar, and can be easily understood by analogy.
Here, orthogonality will be briefly examined taking two or three examples of Walsh codes.
Zeroth through second Walsh code sequences are respectively given as follows.                0th code: {−1, −1, −1, −1, . . . , −1, −1, −1, −1}        1st code: {−1, 1, −1, 1, . . . , −1, 1, −1, 1}        2nd code: {−1, −1, 1, 1, . . . , −1, −1, 1, 1}        
The inner product of the 0th and 1st codes, inner product {0, 1}, can be calculated as follows.inner product {0, 1}=1−1+1−1+ . . . +1−1+1−1=0
Similarly, the inner product of the 1st and 2nd Walsh codes, inner product {1, 2}, and the inner product of the 0th and 2nd codes, inner product {0, 2} can be calculated respectively as follows.inner product {1, 2}=1−1−1+1+ . . . +1−1−1+1=0inner product {0, 2}=1+1−1−1+ . . . +1+1−1−1=0
Since all these inner products are 0, it is clear that the codes of the Walsh function are orthogonal to one another. The other cases can be easily examined, and description of them is omitted.
On the other hand, inner products of the Walsh codes themselves can be calculated as follows. Namely,inner product {0, 0}=1+1+1+1+ . . . +1+1+1+1=32inner product {1, 1}=1+1+1+1+ . . . +1+1+1+1=32inner product {2, 2}=1+1+1+1+ . . . +1+1+1+1=32
When normalized by the code length 32, the inner products of all the code themselves become always unit 1. When Walsh codes are used as code sequences, this means that the same Walsh code can be used as a spread code and the despread code.
Now, it is assumed that, in a certain segment period, the above-mentioned 0th-2nd Walsh codes are used to transmit three pieces of information by multiplex transmission. When the 0th Walsh code is used to transmit a value a, the 1st Walsh code to transmit a value b, and the 2nd Walsh code to transmit a value c, then information inputted to the summing circuit (SUM) 140 (summed signal {0, 1, 2}) is described correspondingly to the chips as follows.summed signal {0, 1, 2}=+a{−1, −1, −1, −1, . . . , −1, −1, −1, −1}+b{−1, 1, −1, 1, . . . , −1, 1, −1, 1}+c{−1, −1, 1, 1, . . . , −1, −1, 1, 1}={−a−b−c, −a+b−c, −a−b+c, −a+b+c, . . . , −a−b−c, −a+b−c, −a−b+c, −a+b+c}  (3)
When the receiving side can correctly receive the summed signal, the received summed signal is multiplied by the despread code, to obtain the value of the primary modulated signal in the corresponding segment, as follows.
Namely, the value corresponding to the 0th Walsh code sequence is given by the inner product of the summed signal {0, 1, 2} and the 0th Walsh signal, as follows. Namely,summed signal {0, 1, 2}-0th Walsh code=−(−a−b−c)−(−a+b−c)−(−a−b+c)−(−a+b+c) −(−a−b−c)−(−a+b−c)−(−a−b+c)−(−a+b+c)=+a+b+c+a−b+c+a+b−c+a−b−c+a+b+c+a−b+c+a+b−c+a−b−c=32a  (4)
Accordingly, it is clear that, when the inner product of the summed signal {0, 1, 2} and the 0th Walsh code is normalized by the code length 32, the value a is correctly received while the values b and c are completely suppressed, realizing correct receiving without interference.
Further, the value corresponding to the 1st Walsh code is given by the inner product of the summed signal {0, 1, 2}and the 1st Walsh code as follows. Namely,summed signal {0, 1, 2}-1st Walsh signal=−(−a−b−c)+(−a+b−c)−(−a−b+c)+(−a+b+c) −(−a−b−c)+(−a+b−c)−(−a−b+c)+(−a+b+c)=+a+b+c−a+b−c+a+b−c−a+b+c +a+b+c−a+b−c+a+b−c−a+b+c=32b  (5)
Accordingly, it is clear that, when the inner product of the summed signal {0, 1, 2} and the 1st Walsh code is normalized by the code length 32, the value b is correctly received, while the values a and c are completely suppressed.
Still further, the value corresponding to the 2nd Walsh code is given by the inner product of the summed signal {0, 1, 2} and the 2nd Walsh code as follows. Namely,summed signal {0, 1, 2}-2nd Walsh code=−(−a−b−c)−(−a+b−c)+(−a−b+c)+(−a+b+c) −(−a−b−c)−(−a+b−c)+(−a−b+c)+(−a+b+c)=+a+b+c+a−b+c−a−b+c−a+b+c+a+b+c+a−b+c−a−b+c−a+b+c=32c  (6)
Accordingly, it is clear that, when the inner product of the summed signal {0, 1, 2} and the 2nd Walsh code is normalized by the code length 32, the value c is correctly received, while the values a and b are completely suppressed.
Thus, as long as spread codes are orthogonal to one another, multiple access in which the number of active channels is same as the number of the spread codes is possible, and communication can be conducted only when the spread codes on both sides of the communication coincide with each other. That is the reason that the Code Division Multiple Access transmission system can be realized using a code, which is the third axis orthogonal to both the time and frequency axes, as a key for communication, in contrast with the Frequency Division Multiple Access transmission system in which a carrier frequency is used as a key and the Time Division Multiple Access transmission system in which a time slot is used as a key. Further, in CDMA, since it can be considered that a code determines a transmission path, a channel is established for each spread code. Thus, frequently, the number of the spread codes is called the number of channels.
In FIG. 31, since the primary modulated wave has positive values 0-1 in the 0th segment of the symbol 1, and negative values 0-−1 in the 1st segment as shown in FIG. 30, the sign of the corresponding chip values in the 0th segment of the symbol 1 changes from minus to plus alternately and the sign of the chip values in the 1st segment changes from plus to minus alternately.
When the code length is 32, the chip rate of the spread codes becomes 32 ksps-4 segments-32 chip/segment=4.096 M chips/sec. (hereinafter, chips/sec. is written as cps).
All the spread codes changes synchronously with one another in each chip interval, and thus the summed signal whose signal value in a chip interval is the summation of the hip values becomes a rectangular wave of a constant value within a chip interval. Accordingly, both in the case of the maximum information rate of 2 Mbps in which 32 channels are used for simultaneous transmission and in the case of the minimum information rate in which 1 channel is used for transmission at 64 kbps, the chip rate is always constant at 4.096 Mcps irrespective of transmission rates of information.
Thus, as shown in FIG. 26, a plurality of spread signals corresponding to information signals and necessary control signal are generated by the spreading circuits (SS) 120-12n, using spread codes outputted from the spread code generating circuits (CG) 130-13n and orthogonal to one another. Then, the summation of the plurality of spread codes is obtained by the summing circuit (SUM) 140 and, if necessary, the summed signal obtained is subjected to the frequency conversion and power amplification in the transmitting circuit (TX), to be transmitted as a CDMA signal.
Here, it is assumed that the number (n+1) of the spreading circuits (SS) 120-12n is equal to or less than the spread factor, i.e., the length N of spread code sequence.
In order to transmit only the sum total of the summed signal, a transmission band of half the chip rate, i.e. 2.048 MHz is sufficient from the Shannon's sampling theorem. However, it is necessary to obtain the inner product of the received chip waveform and the despread code for despreading, and thus, it difficult to ensure the orthogonality between the spread codes by transmitting only the sum total. Because of this, it is desirable to transmit the rectangular waveform of the summed signal as faithfully as possible, and accordingly the band width of 2.048 MHz or more is used.
Accurate transmission of a rectangular waveform of a CDMA signal requires a frequency several times as high as the chip rate. However, as shown in FIG. 26, in many cases, band-pass filter operation is carried out as a function of the bandlimiting circuit (BPF) 141, to limit the frequency band width to the degree of the chip rate.
As shown in FIG. 26, if necessary, the CDMA signal is subjected to suitable processing such as conversion to a target frequency and power amplification in the transmitting circuit (TX) 142, and thereafter, radiated through an antenna. As the target frequency, a frequency domain of 2 GHz is frequently used, and accordingly, the following discussion is directed to CDMA transmission in this frequency domain of 2 GHz. However, the other frequency band is similar and can be easily conjectured, and their description is omitted. Further, the above-mentioned control signal does not directly relate to the present invention, and therefore, its further description is omitted.
Here, usually, a radio wave transmitted through the transmitting circuit (TX) 142 as described above is seldom transmitted through an ideal radio wave propagation path. In the mobile communication such as the automobile telephone and the pedestrian telephone, a transmitter itself moves so that the Doppler shift is generated and the carrier frequency deviates. Or, in many cases, a radio wave is received via a plurality of propagation paths. Accordingly, the phase and amplitude of the received wave changes with time (which is called the fading phenomenon, and in particular called the Rayleigh fading in a poor transmission environment causing the phase change of uniform distribution and making the amplitude have the Rayleigh distribution). Or, a radio wave is strongly reflected by building walls etc., and accordingly, it arrives at various points of time through different propagation paths of various lengths. In addition, in many cases, these strongly-reflected waves themselves are transmitted through multi-ray propagation paths with each arrival wave suffering the Rayleigh fading phenomenon independently.
On the receiving side, a CDMA receiver comprises main functional circuits, for example, for reception, synchronous detection, reception control, demodulation, despread, phase correction, judgment, etc.
In FIG. 32, the reception control circuit (CNT) 204 detects various control signals required for control of the receiver, and outputs a plurality of despread code sequences required for receiving. The synchronous detection circuit (SYNC) 203 outputs a regenerated carrier wave, a chip synchronizing signal, a segment synchronizing signal, a symbol synchronizing signal, etc. from the received signal.
The demodulator circuit (deMOD) 201 has the structure shown in FIG. 33. In that figure, the received wave applied to an input terminal 2010 connected to the receiving circuit (RX) 200 is inputted to the multipliers 2011 and 2012. Here, the demodulator circuit (deMOD) 201 , which generally utilizes the synchronous detection system, obtains the product of the regenerated carrier wave 202 and the received wave by the multiplier 2011, then accumulates the product for each carrier cycle by the accumulator 2014 to obtain the inner product of each carrier cycle, takes in the obtained inner products into the latch register (REG) 2016 to hold them only for their carrier cycle periods, and outputs the values held in the latch register (REG) 2016 as in-phase components i(t) of the modulated signal of the primary modulated wave, for respective carrier cycle periods. At the same time, the demodulator circuit (deMOD) 201 obtains an orthogonal carrier signal by shifting the regenerated carrier wave 202 by 90 degrees in phase by the phase shifter 2013, to obtain the product of the orthogonal carrier signal and the received wave by the multiplier 2012. Then, the product is accumulated for each carrier cycle by the accumulator 2015 to obtain the inner product for each carrier cycle. The obtained inner products are taken into the latch register (REG) 2017 to hold them only for their carrier cycle periods. The values held in the latch register (REG) 2017 are outputted as quadrature components q(t) of the modulated signal of the primary modulated wave, for respective carrier cycle periods. The signal R inputted to the accumulators 2014, 2015 is an accumulation reset signal inputted from the control terminal 2018 for each carrier cycle. At every trailing edge of this accumulation reset signal R, the accumulated values of the accumulator 2014, 2015 are reset to zero. Further, the signal R inputted to the latch registers (REG) 2016, 2017 are the accumulation reset signal inputted from the control terminal 2018 for each carrier cycle. At every leading edge of this accumulation signal R, the accumulators 2016, 2017 hold the inputted values.
In FIG. 32, the in-phase components i(t) and quadrature components q(t) of the demodulated signal from the demodulator circuit 201 are inputted to (n+1) despreading circuits (deSS) 210-21n. FIG. 34 shows an example of these despreading circuits (deSS) 210-21n. An in-phase component i(t) and quadrature component q(t) of the demodulated signal are inputted to the input terminals 2100, 2101, respectively. The multipliers 2102, 2103 obtain the products of the in-phase component i(t) or quadrature component q(t) of the demodulated signal and the i-th despread code sequence inputted from the terminal 22i, in accordance with the chip synchronizing signal, and obtain the accumulation of the product for each segment, in accordance with the segment synchronizing signal. Here, the i-th despread code sequence means the despread code sequence corresponding to the i-th spread code used on the transmitting side. When the Walsh function is used, the despread code sequence and the spread code sequence are equal to each other.
Accordingly, in FIG. 32, the corresponding despread codes are inputted to the respective terminals 220-22n of the despreading circuits 210-21n. Then, outputs of the multipliers 2102, 2103 are accumulated in the accumulators 2014, 2015. The accumulation reset signal R is inputted to the accumulators 2104, 2105 from the terminal 2110, for each segment. The outputs of the accumulators 2104, 2105 are each normalized by the code length, held by the latch registers (REG) 2106, 2107 for the segment interval, and outputted from the output terminals 2108, 2109 as the in-phase component Ii′(t) and quadrature component Qi′(t) of the despread signal.
Here, since the spread codes are orthogonal to one another, when the desperad code coincides with the spread code of the transmission, despreading circuits 210-21n output a finite value, realizing correct receiving. On the other hand, when the despread code does not coincide with the spread code of the transmission, the despreading circuits 210-21n always output zero, and thus, does not effectively output the received signal.
The in-phase components Ii′(t) and quadrature components Qi′(t) of the despread signal relating to n information channels of the simultaneous multiple access system are outputted from the despreading circuits 211-21n. The in-phase component I0′(t) and quadrature component Q0′(t) of the despread signal relating to the pilot signal common to those n channels are outputted from the despreading circuit 210.
These despread signals are each subject to disturbances such as phase error, amplitude distortion, delay, and the like, during transmission. By transmitting a pilot spread signal obtained by spreading a primary modulated wave of phase information of a known value, for example “0”, and by measuring the error between the known value and a phase value detected on the receiving side, it is logically possible to generally know the phase error due to the disturbances that have arisen during the transmission. Accordingly; as shown in FIG. 32, in many cases, is employed the pilot system in which one channel of a pilot signal for transmitting a known value is added to the n channels of information, to generally correct disturbances during transmission.
Accordingly, the following description is directed to the case in which one pilot channel is added to n information channels. However, a case in which one pilot channel is added to one information channel and a case in which an in-phase component and quadrature component of a primary modulated wave in each spread signal are assigned respectively to an information channel and a pilot channel are similar and can be easily understood by analogy. Therefore, description of such cases is omitted.
In FIG. 32, outputs of the despreading circuits (deSS) 211-21n and output of the despreading circuit (deSS) 210 are led to the phase correction circuits (CMP) 231-23n. FIG. 35 shows an example of cofiguration of those phase correction circuits (CMP). The in-phase component Ii′(t) and quadrature component Qi′(t) of the despreading circuit (deSS) 23i are inputted to the input terminals 2300 and 2301, respectively. Further, the in-phase component Ii′(t) and quadrature component Q0′(t) of the despreading circuit 230 are inputted to the input terminals 2302 and 2303, respectively. Then, the in-phase component Ii′(t) of the information channel i is inputted to the multipliers 2310 and 2311, and the quadrature component Qi′(t) of the information channel i is inputted to the multipliers 2312 and 2313. The in-phase component I0′(t) of the pilot channel is inputted to the multipliers 2310 and 2312, and the quadrature component Q0′(t) of the pilot channel is inputted to the multipliers 2313 and 2311. The adder 2320 outputs the sum of the outputs of the multipliers 2310 and 2313, as the in-phase component Ii(t) of the phase correction signal, to the terminal 2340. Further, the adder 2321 outputs the difference between the output of the multiplier 2312 and the output of the multiplier 2311, as the quadrature component Qi(t) of the phase correction signal, to the terminal 2341.
In FIG. 32, further, the outputs of the phase correction circuits (CMP) 231-23n are led to the decision circuits (DEC) 241-24n. When the in-phase component Ii(t) and quadrature component Qi(t) of the phase correction signal are inputted, the decision circuits (DEC) 241-24n each obtain a phase angle and a received symbol Si(t) of dibit defined correspondingly to the received phase angle obtained, and output it as the corresponding information to the terminal 251-25n. 
Next, a series of processing in the receiver shown in FIG. 32 will be described in detail, using mathematics expressions. The output of the receiving circuit (RX) 200, i.e. the received signal r(t) is written as the equation 7.                               r          ⁢                                           ⁢                      (            t            )                          =                              ∑                          j              =              1                        m                    ⁢                                           ⁢                                    ∑                              i                =                0                            n                        ⁢                                                   ⁢                                          a                j                            ⁢                                                           ⁢                              (                t                )                            ⁢                                                           ⁢                              W                i                            ⁢                              {                                  t                  -                                                            δ                      l                                        ⁢                                                                                   ⁢                                          (                      t                      )                                                                      }                            ⁢                                                           ⁢                              cos                ⁡                                  [                                                                                    {                                                                              ω                            c                                                    ±                                                      Δ                            ⁢                                                                                                                   ⁢                                                          ω                              j                                                        ⁢                                                                                                                   ⁢                                                          (                              t                              )                                                                                                      }                                            ⁢                                              {                                                  t                          -                                                                                    δ                              j                                                        ⁢                                                                                                                   ⁢                                                          (                              t                              )                                                                                                      }                                                              +                                                                  θ                        i                                            ⁢                                              {                                                  i                          -                                                                                    δ                              j                                                        ⁢                                                                                                                   ⁢                                                          (                              t                              )                                                                                                      }                                                              +                                          Δ                      ⁢                                                                                           ⁢                                              ϕ                        j                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                                              ]                                                                                        (        7        )            
Here, the suffix j indicates j-th propagation path of multi-ray Rayleigh fading, when, for the sake of convenience, the propagation paths are expressed as 1st, 2nd, . . . , m-th propagation paths in order of average received power. The letter m indicates the total number of the multi-ray propagation paths;
The suffix i (i=0, 1, . . . , n) indicates the number of the code sequence of the Walsh function, and here n means the total number of the code sequences of the Walsh function used for transmission;
δj(t) indicates a delay time in the propagation path j;
aj(t) indicates an amplitude distortion in the propagation path j. It is assumed that aj(t) is given by aj(t)=αj(t)kj(t). Here, αj(t) is a fading amplitude distortion in the propagation path j, and it is assumed that the amplitude shows the Rayleigh distribution and the maximum variable frequency is defined by the fading frequency. Further, kj(t) is the propagation gain of the propagation path j;
Δφj(t) indicates the fading phase error of the propagation path j, and its value is uniformly distributed between −180 degrees and 180 degrees. It is assumed that the upper limit of the variable frequency is defined by the fading frequency;
Wi(t) is the value of the i-th spread code sequence at the time t, the i-th spread code sequence changing correspondingly to the chip;
ωc is defined by ωc=2πfc, where fc, is the carrier frequency;
Δωj(t) indicates the frequency deviation caused by Doppler shift in the propagation path j; and
θi(t) indicates the information phase of the primary modulated wave corresponding to the i-th code sequence.
Here, in the synchronous detection circuit (SYNC) whose details are not shown, the carrier signal is regenerated in accordance with the components that have passed a plurality of propagation paths and contained in the received wave. These regenerated carrier in-phase wave c(t) and regenerated carrier quadrature wave s(t) are respectively given as follows.c(t)=cos [ωc{t−δ(t)}+Δφ(t)]  (8)s(t)=sin [ωc{t−δ(t)}+Δφ(t)]  (9)where δ(t) is a time delay of the regenerated carrier wave, and Δφ(t) is a phase error of the regenerated carrier wave.
The outputs of the demodulator circuit (deMOD) 201 , i.e., the in-phase component i(t) and quadrature component q(t) of the demodulated signal are respectively given as the inner products of the received signal r(t) and the regenerated carrier in-phase wave c(t) or the regenerated carrier quadrature wave s(t) as follows.                               i          ⁢                                           ⁢                      (            t            )                          =                              1            τ                    ⁢                                           ⁢                                    ∫              t                              1                +                τ                                      ⁢                          r              ⁢                                                           ⁢                              (                t                )                            ⁢                                                           ⁢              c              ⁢                                                           ⁢                              (                d                )                            ⁢                                                           ⁢                              ⅆ                t                                                                        (        10        )                                          q          ⁢                                           ⁢                      (            t            )                          =                              1            τ                    ⁢                                           ⁢                                    ∫              t                              1                +                τ                                      ⁢                          r              ⁢                                                           ⁢                              (                t                )                            ⁢                                                           ⁢              s              ⁢                                                           ⁢                              (                d                )                            ⁢                                                           ⁢                              ⅆ                t                                                                        (        11        )            where τ is the carrier cycle period, i.e., the reciprocal of the carrier frequency.
The carrier cycle is small in comparison with the chip cycle, and furthermore, the fading cycle and the frequency deviation of the Doppler shift are sufficiently small in comparison with the carrier frequency. Accordingly, it can be assumed that the value of the spread code, the fading phase distortion, and the fading amplitude distortion are maintained at constant values within a carrier cycle. Here, the fading cycle means the reciprocal of the fading frequency.
Thus, the equations 10 and 11 can be calculated as follows.                               i          ⁢                                           ⁢                      (            t            )                          =                              1                          2              ⁢                                                           ⁢              τ                                ⁢                                           ⁢                                    ∫              t                              1                +                τ                                      ⁢                                          ∑                                  j                  =                  1                                m                            ⁢                                                           ⁢                                                ∑                                      i                    =                    0                                    n                                ⁢                                                                   ⁢                                                      α                    j                                    ⁢                                                                           ⁢                                      (                    t                    )                                    ⁢                                                                           ⁢                                      W                    j                                    ⁢                                                                           ⁢                                                            {                                              t                        -                                                                              δ                            j                                                    ⁢                                                                                                           ⁢                                                      (                            t                            )                                                                                              }                                        ·                                          [                                                                        cos                          ⁢                                                      {                                                                                          2                                ⁢                                                                                                                                   ⁢                                                                  ω                                  c                                                                ⁢                                                                                                                                   ⁢                                t                                                            +                                                                                                                                    θ                                    i                                                                    ⁢                                                                                                                                           ⁢                                                                      (                                                                          t                                      -                                                                                                                        δ                                          j                                                                                ⁢                                                                                                                                                                   ⁢                                                                                  (                                          t                                          )                                                                                                                                                      )                                                                                                  ±                                                                  Δ                                  ⁢                                                                                                                                           ⁢                                                                      ω                                    j                                                                    ⁢                                                                                                                                           ⁢                                                                      (                                    t                                    )                                                                    ⁢                                                                                                                                           ⁢                                                                      (                                                                          t                                      -                                                                                                                        δ                                          j                                                                                ⁢                                                                                                                                                                   ⁢                                                                                  (                                          t                                          )                                                                                                                                                      )                                                                                                                              +                                                              Δ                                ⁢                                                                                                                                   ⁢                                                                  ϕ                                  j                                                                ⁢                                                                                                                                   ⁢                                                                  (                                  t                                  )                                                                                            +                                                              Δ                                ⁢                                                                                                                                   ⁢                                ϕ                                ⁢                                                                                                                                   ⁢                                                                  (                                  t                                  )                                                                                            -                                                                                                ω                                  c                                                                ⁢                                                                                                                                   ⁢                                                                  (                                                                                                                                                    δ                                        j                                                                            ⁢                                                                                                                                                           ⁢                                                                              (                                        t                                        )                                                                                                              +                                                                          δ                                      ⁢                                                                                                                                                           ⁢                                                                              (                                        t                                        )                                                                                                                                              )                                                                                                                      }                                                                          +                                                  cos                          ⁢                                                      {                                                                                                                                                                θ                                    i                                                                    ⁢                                                                                                                                           ⁢                                                                      (                                                                          t                                      -                                                                                                                        δ                                          j                                                                                ⁢                                                                                                                                                                   ⁢                                                                                  (                                          t                                          )                                                                                                                                                      )                                                                                                  ±                                                                  Δ                                  ⁢                                                                                                                                           ⁢                                                                      ω                                    j                                                                    ⁢                                                                                                                                           ⁢                                                                      (                                    t                                    )                                                                    ⁢                                                                                                                                           ⁢                                                                      (                                                                          t                                      -                                                                                                                        δ                                          j                                                                                ⁢                                                                                                                                                                   ⁢                                                                                  (                                          t                                          )                                                                                                                                                      )                                                                                                                              +                                                              (                                                                                                      Δ                                    ⁢                                                                                                                                                   ⁢                                                                          ϕ                                      j                                                                        ⁢                                                                                                                                                   ⁢                                                                          (                                      t                                      )                                                                                                        -                                                                      Δ                                    ⁢                                                                                                                                                   ⁢                                    ϕ                                    ⁢                                                                                                                                                   ⁢                                                                          (                                      t                                      )                                                                                                                                      )                                                            -                                                                                                ω                                  c                                                                ⁢                                                                                                                                   ⁢                                                                  (                                                                                                                                                    δ                                        j                                                                            ⁢                                                                                                                                                           ⁢                                                                              (                                        t                                        )                                                                                                              +                                                                          δ                                      ⁢                                                                                                                                                           ⁢                                                                              (                                        t                                        )                                                                                                                                              )                                                                                                                      }                                                                                              ]                                                        ⁢                                                                           ⁢                                      ⅆ                    t                                                                                                          (        12        )            
With respect to the variables for the trigonometric functions within the brackets [ ], variables other than the component of the carrier are almost constants within a carrier cycle. Accordingly, with respect to the in-phase component i(t) of the demodulated signal, the integral of the first term within the brackets [ ] converges to zero, and the second term becomes almost the average.                               i          ⁢                                           ⁢                      (            t            )                          =                              1            2                    ⁢                                           ⁢                                    ∑                              j                =                1                            m                        ⁢                                                   ⁢                                          ∑                                  i                  =                  0                                n                            ⁢                                                           ⁢                                                α                  j                                ⁢                                                                   ⁢                                  (                  t                  )                                ⁢                                                                   ⁢                                  W                  j                                ⁢                                  {                                      t                    -                                                                  δ                        j                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                                              }                                ⁢                                  cos                  ⁡                                      [                                                                                            θ                          i                                                ⁢                                                                                                   ⁢                                                  (                                                      t                            -                                                                                          δ                                j                                                            ⁢                                                                                                                           ⁢                                                              (                                t                                )                                                                                                              )                                                                    +                                                                        φ                          j                                                ⁢                                                                                                   ⁢                                                  (                          t                          )                                                                                      ]                                                                                                          (        13        )            whereφj(t)=±Δωj(t){t−δj(t)}+{Δφj(t)−Δφ(t)}−ωc{δj(t)−δ(t)}  (14)
Similarly, the quadrature component q(t) of the demodulated signal is obtained as follows.                               q          ⁡                      (            t            )                          =                                            -                              1                                  2                  ⁢                                                                           ⁢                  τ                                                      ⁢                                                   ⁢                                          ∫                t                                  1                  +                  τ                                            ⁢                                                ∑                                      j                    =                    1                                    m                                ⁢                                                                   ⁢                                                      ∑                                          i                      =                      0                                        n                                    ⁢                                                                           ⁢                                                            α                      j                                        ⁢                                                                                   ⁢                                          (                      t                      )                                        ⁢                                                                                   ⁢                                          W                      j                                        ⁢                                                                                   ⁢                                                                  {                                                  t                          -                                                                                    δ                              j                                                        ⁢                                                                                                                   ⁢                                                          (                              t                              )                                                                                                      }                                            ·                                              [                                                                              sin                            ⁢                                                          {                                                                                                2                                  ⁢                                                                                                                                           ⁢                                                                      ω                                    c                                                                    ⁢                                                                                                                                           ⁢                                  t                                                                +                                                                                                                                            θ                                      i                                                                        ⁢                                                                                                                                                   ⁢                                                                          (                                                                              t                                        -                                                                                                                              δ                                            j                                                                                    ⁢                                                                                                                                                                           ⁢                                                                                      (                                            t                                            )                                                                                                                                                              )                                                                                                        ±                                                                      Δ                                    ⁢                                                                                                                                                   ⁢                                                                          ω                                      j                                                                        ⁢                                                                                                                                                   ⁢                                                                          (                                      t                                      )                                                                        ⁢                                                                                                                                                   ⁢                                                                          (                                                                              t                                        -                                                                                                                              δ                                            j                                                                                    ⁢                                                                                                                                                                           ⁢                                                                                      (                                            t                                            )                                                                                                                                                              )                                                                                                                                      +                                                                  Δ                                  ⁢                                                                                                                                           ⁢                                                                      ϕ                                    j                                                                    ⁢                                                                                                                                           ⁢                                                                      (                                    t                                    )                                                                                                  +                                                                  Δ                                  ⁢                                                                                                                                           ⁢                                  ϕ                                  ⁢                                                                                                                                           ⁢                                                                      (                                    t                                    )                                                                                                  -                                                                                                      ω                                    c                                                                    ⁢                                                                                                                                           ⁢                                                                      (                                                                                                                                                            δ                                          j                                                                                ⁢                                                                                                                                                                   ⁢                                                                                  (                                          t                                          )                                                                                                                    +                                                                              δ                                        ⁢                                                                                                                                                                   ⁢                                                                                  (                                          t                                          )                                                                                                                                                      )                                                                                                                              }                                                                                +                                                      sin                            ⁢                                                          {                                                                                                                                                                          θ                                      i                                                                        ⁢                                                                                                                                                   ⁢                                                                          (                                                                              t                                        -                                                                                                                              δ                                            j                                                                                    ⁢                                                                                                                                                                           ⁢                                                                                      (                                            t                                            )                                                                                                                                                              )                                                                                                        ±                                                                      Δ                                    ⁢                                                                                                                                                   ⁢                                                                          ω                                      j                                                                        ⁢                                                                                                                                                   ⁢                                                                          (                                      t                                      )                                                                        ⁢                                                                                                                                                   ⁢                                                                          (                                                                              t                                        -                                                                                                                              δ                                            j                                                                                    ⁢                                                                                                                                                                           ⁢                                                                                      (                                            t                                            )                                                                                                                                                              )                                                                                                                                      +                                                                  (                                                                                                            Δ                                      ⁢                                                                                                                                                           ⁢                                                                              ϕ                                        j                                                                            ⁢                                                                                                                                                           ⁢                                                                              (                                        t                                        )                                                                                                              -                                                                          Δ                                      ⁢                                                                                                                                                           ⁢                                      ϕ                                      ⁢                                                                                                                                                           ⁢                                                                              (                                        t                                        )                                                                                                                                              )                                                                -                                                                                                      ω                                    c                                                                    ⁢                                                                                                                                           ⁢                                                                      (                                                                                                                                                            δ                                          j                                                                                ⁢                                                                                                                                                                   ⁢                                                                                  (                                          t                                          )                                                                                                                    +                                                                              δ                                        ⁢                                                                                                                                                                   ⁢                                                                                  (                                          t                                          )                                                                                                                                                      )                                                                                                                              }                                                                                                      ]                                                              ⁢                                                                                   ⁢                                          ⅆ                      t                                                                                                    ≅                                    -                              1                2                                      ⁢                                                   ⁢                                          ∑                                  j                  =                  1                                m                            ⁢                                                           ⁢                                                ∑                                      i                    =                    0                                    n                                ⁢                                                                   ⁢                                                      α                    j                                    ⁢                                                                           ⁢                                      (                    t                    )                                    ⁢                                                                           ⁢                                      W                    j                                    ⁢                                                                           ⁢                                      (                                          t                      -                                                                        δ                          j                                                ⁢                                                                                                   ⁢                                                  (                          t                          )                                                                                      }                                    ⁢                                                                           ⁢                                      sin                    ⁡                                          [                                                                                                    θ                            i                                                    ⁢                                                                                                           ⁢                                                      (                                                          t                              -                                                                                                δ                                  j                                                                ⁢                                                                                                                                   ⁢                                                                  (                                  t                                  )                                                                                                                      )                                                                          +                                                                              φ                            j                                                    ⁢                                                                                                           ⁢                                                      (                            t                            )                                                                                              ]                                                                                                                              (        15        )            
The in-phase component Id′(t) or quadrature component Qd′(t) of the despread code of the channel d outputted from the despreading circuit (deSS) 210-21n are given as the inner product between the despread code sequence Wd and the in-phase component i(t) or quadrature component q(t) of the demodulated signal within a segment, as follows.                                           I            d            ′                    ⁢                                           ⁢                      (            t            )                          =                              1                          2              ⁢              N                                ⁢                                           ⁢                                    ∑                              k                =                0                                            N                -                1                                      ⁢                                                   ⁢                                          ∑                                  j                  =                  1                                m                            ⁢                                                           ⁢                                                ∑                                      l                    =                    0                                    n                                ⁢                                                                   ⁢                                                      α                    j                                    ⁢                                                                           ⁢                                      (                    t                    )                                    ⁢                                                                           ⁢                                      W                    i                                    ⁢                                      {                                          t                      +                                              k                        ⁢                                                                                                   ⁢                        λ                                            -                                                                        δ                          j                                                ⁢                                                                                                   ⁢                                                  (                          t                          )                                                                                      }                                    ⁢                                      W                    d                                    ⁢                                                            {                                              t                        +                                                  k                          ⁢                                                                                                           ⁢                          λ                                                -                                                                              δ                            j                                                    ⁢                                                                                                           ⁢                                                      (                            t                            )                                                                                              }                                        ·                                          cos                      ⁡                                              [                                                                                                            θ                              i                                                        ⁢                                                                                                                   ⁢                                                          (                                                              t                                +                                                                  k                                  ⁢                                                                                                                                           ⁢                                  λ                                                                -                                                                                                      δ                                    j                                                                    ⁢                                                                                                                                           ⁢                                                                      (                                    t                                    )                                                                                                                              )                                                                                +                                                                                    φ                              j                                                        ⁢                                                                                                                   ⁢                                                          (                                                              t                                +                                                                  k                                  ⁢                                                                                                                                           ⁢                                  λ                                                                                            )                                                                                                      ]                                                                                                                                                    (        16        )                                                      Q            d            ′                    ⁢                                           ⁢                      (            t            )                          =                              1                          2              ⁢              N                                ⁢                                           ⁢                                    ∑                              k                =                0                                            N                -                1                                      ⁢                                                   ⁢                                          ∑                                  j                  =                  1                                m                            ⁢                                                           ⁢                                                ∑                                      i                    =                    0                                    n                                ⁢                                                                   ⁢                                                      α                    j                                    ⁢                                                                           ⁢                                      (                    t                    )                                    ⁢                                                                           ⁢                                      W                    i                                    ⁢                                      {                                          t                      +                                              k                        ⁢                                                                                                   ⁢                        λ                                            -                                                                        δ                          j                                                ⁢                                                                                                   ⁢                                                  (                          t                          )                                                                                      }                                    ⁢                                      W                    d                                    ⁢                                                            {                                              t                        +                                                  k                          ⁢                                                                                                           ⁢                          λ                                                -                                                                              δ                            j                                                    ⁢                                                                                                           ⁢                                                      (                            t                            )                                                                                              }                                        ·                                          sin                      ⁡                                              [                                                                                                            θ                              i                                                        ⁢                                                                                                                   ⁢                                                          (                                                              t                                +                                                                  k                                  ⁢                                                                                                                                           ⁢                                  λ                                                                -                                                                                                      δ                                    j                                                                    ⁢                                                                                                                                           ⁢                                                                      (                                    t                                    )                                                                                                                              )                                                                                +                                                                                    φ                              j                                                        ⁢                                                                                                                   ⁢                                                          (                                                              t                                +                                                                  k                                  ⁢                                                                                                                                           ⁢                                  λ                                                                                            )                                                                                                      ]                                                                                                                                                    (        17        )            where 0≦d≦n, and λ is the chip cycle and N is the code length.φj(t+kλ)=±Δωj(t){t+kλ−δj(t)}+{Δφj(t)−Δφ(t)}−ω{δj(t)−δ(t)}  (18)
When, in the equations 16 and 17, the despread code Wd of the reception channel d correctly coincides the transmission code Wi, then, the in-phase component Ii′(t) and quadrature component Qi′(t) of the despread signal corresponding to the i-th spread code are respectively given as follows.                                           I            i            ′                    ⁢                                           ⁢                      (            t            )                          ≅                              ∑                          j              =              1                        m                    ⁢                                           ⁢                                                                                          a                    ~                                    j                                ⁢                                                                   ⁢                                  (                  t                  )                                            2                        ⁢                                                   ⁢            cos            ⁢                          {                                                                    θ                    i                                    ⁢                                                                           ⁢                                      (                                          t                      -                                                                        δ                          j                                                ⁢                                                                                                   ⁢                                                  (                          t                          )                                                                                      )                                                  +                                                                            ψ                      ~                                        i                                    ⁢                                                                           ⁢                                      (                    t                    )                                                  +                                                                            φ                      ~                                        j                                    ⁢                                                                           ⁢                                      (                    t                    )                                                              }                                                          (        19        )                                                      Q            i            ′                    ⁢                                           ⁢                      (            t            )                          ≅                              ∑                          j              =              1                        m                    ⁢                                           ⁢                                                                                          a                    ~                                    j                                ⁢                                                                   ⁢                                  (                  t                  )                                            2                        ⁢                                                   ⁢            sin            ⁢                          {                                                                    θ                    i                                    ⁢                                                                           ⁢                                      (                                          t                      -                                                                        δ                          j                                                ⁢                                                                                                   ⁢                                                  (                          t                          )                                                                                      )                                                  +                                                                            ψ                      ~                                        i                                    ⁢                                                                           ⁢                                      (                    t                    )                                                  +                                                                            φ                      ~                                        j                                    ⁢                                                                           ⁢                                      (                    t                    )                                                              }                                                          (        20        )            where    ãj(t) is an expected value, within a segment, of the amplitude distortion aj(t) in the j-th propagation path;    {tilde over (ψ)}i(t) is an expected value, within a segment, of the phase error φi(t) having the frequency characteristics intrinsic to the spread code sequence Wi;    {tilde over (φ)}j(t) is an expected value, within a segment, of the phase error φj(t) in the j-th propagation path,{tilde over (φ)}j(t)=±Δ{tilde over (ω)}j(t){t−{tilde over (δ)}j(t)}+{Δ{tilde over (φ)}j(t)−Δ{tilde over (φ)}(t)}−ωc{{tilde over (δ)}j(t)−{tilde over (δ)}(t)}  (21)andãj(t)=ãj(t){tilde over (k)}j(t)
ãj(t) is an expected value, within a segment, of the fading amplitude distortion in the propagation path j;
{tilde over (k)}j(t) is an expected value, within a segment, of the propagation gain in the propagation path j;
Δ{tilde over (ω)}j(t) is an expected value, within a segment, of the Doppler shift in the propagation path j;
Δ{tilde over (φ)}j(t) is an expected value, within a segment, of the fading phase error in the propagation path j;
{tilde over (δ)}j(t) is an expected value, within a segment, of the propagation delay in the propagation path j;
Δ{tilde over (φ)}(t) is an expected value, within a segment, of the phase error of the regenerated carrier wave; and
{tilde over (δ)}(t) is an expected value, within a segment, of the delay of the regenerated carrier wave.
The spread code sequence Wi of the received wave coming through an inferior propagation path has already been subjected to distortion, and thus, an error φi(t) intrinsic to the spread code sequence Wi is generated in the despread signal. Further, the in-phase component Ii′(t) and quadrature component Qi′(t) of the despread signal for the channel i in the two-ray Rayleigh fading environment are given by the following simple equation.Ii′(t)≅{tilde over (β)}(t)cos {θi(t−{tilde over (δ)}1(t))+{tilde over (ψ)}i(t)+{tilde over (ψ)}(t)}  (22)Qi′(t)≅−{tilde over (β)}(t)sin {θi(t−{tilde over (δ)}1(t))+{tilde over (ψ)}i(t)+{tilde over (ψ)}(t)}  (23)where                                           β            ~                    ⁢                                           ⁢                      (            t            )                          =                              1            2                    ⁢                                           ⁢                                                                                          a                    ~                                    1                                ⁢                                                                   ⁢                                                      (                    t                    )                                    2                                            +                                                                    a                    ~                                    2                                ⁢                                                                   ⁢                                                      (                    t                    )                                    2                                            +                              2                ⁢                                                                   ⁢                                                      a                    ~                                    1                                ⁢                                                                   ⁢                                  (                  t                  )                                ⁢                                                                   ⁢                                                      a                    ~                                    2                                ⁢                                                                   ⁢                                  (                  t                  )                                ⁢                                                                   ⁢                cos                ⁢                                  {                                                                                                              φ                          ~                                                1                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                              -                                                                                            φ                          ~                                                2                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                                              }                                                                                        (        24        )                                                      ϑ            ~                    ⁢                                           ⁢                      (            t            )                          =                              tan                          -              1                                ⁡                      [                                                                                                      a                      ~                                        1                                    ⁢                                                                           ⁢                                      (                    t                    )                                    ⁢                                                                           ⁢                  sin                  ⁢                                      {                                                                                            φ                          ~                                                1                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                              }                                                  +                                                                            a                      ~                                        2                                    ⁢                                                                           ⁢                                      (                    t                    )                                    ⁢                                                                           ⁢                  sin                  ⁢                                      {                                                                                            φ                          ~                                                2                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                              }                                                                                                                                          a                      ~                                        1                                    ⁢                                                                           ⁢                                      (                    t                    )                                    ⁢                                                                           ⁢                  cos                  ⁢                                      {                                                                                            φ                          ~                                                1                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                              }                                                  +                                                                            a                      ~                                        2                                    ⁢                                                                           ⁢                                      (                    t                    )                                    ⁢                                                                           ⁢                  cos                  ⁢                                      {                                                                                            φ                          ~                                                2                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                              }                                                                        ]                                              (        25        )            
Further, the equation 24 can be expressed using the 2nd propagation path to the 1st propagation path ratio P21(t) of the instantaneous power to obtain the following equation.                                           β            ~                    ⁢                                           ⁢                      (            t            )                          =                                                                              a                  ~                                1                            ⁢                                                           ⁢                              (                t                )                                      2                    ⁢                                           ⁢                                    1              +                                                P                  21                  2                                ⁢                                                                   ⁢                                  (                  t                  )                                            +                              2                ⁢                                  P                  21                                ⁢                                                                   ⁢                                  (                  t                  )                                ⁢                                                                   ⁢                cos                ⁢                                  {                                                                                                              φ                          ~                                                1                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                              -                                                                                            φ                          ~                                                2                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                                              }                                                                                        (        26        )            where the instantaneous power ratio P21(t) is defined by             P      21        ⁢                   ⁢          (      t      )        =                              a          ~                2            ⁢                           ⁢              (        t        )                                      a          ~                1            ⁢                           ⁢              (        t        )            
Similarly, the equation 25 can be expressed as follows, using the instantaneous power ratio on its right side.                                           ϑ            ~                    ⁢                                           ⁢                      (            t            )                          =                              tan                          -              1                                ⁡                      [                                                            sin                  ⁢                                      {                                                                                            φ                          ~                                                1                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                              }                                                                    cos                  ⁢                                      {                                                                                            φ                          ~                                                2                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                              }                                                              ⁢                                                           ⁢                                                1                  +                                                            P                      21                                        ⁢                                                                                   ⁢                                          (                      t                      )                                        ⁢                                                                                   ⁢                                                                  sin                        ⁢                                                  {                                                                                                                    φ                                ~                                                            2                                                        ⁢                                                                                                                   ⁢                                                          (                              t                              )                                                                                }                                                                                            sin                        ⁢                                                  {                                                                                                                    φ                                ~                                                            1                                                        ⁢                                                                                                                   ⁢                                                          (                              t                              )                                                                                }                                                                                                                                      1                  +                                                            P                      21                                        ⁢                                                                                   ⁢                                          (                      t                      )                                        ⁢                                                                                   ⁢                                                                  cos                        ⁢                                                  {                                                                                                                    φ                                ~                                                            2                                                        ⁢                                                                                                                   ⁢                                                          (                              t                              )                                                                                }                                                                                            cos                        ⁢                                                  {                                                                                                                    φ                                ~                                                            1                                                        ⁢                                                                                                                   ⁢                                                          (                              t                              )                                                                                }                                                                                                                                          ]                                              (        27        )            
The incoming wave of the 1st propagation path is called a desired wave (D wave) and an incoming wave of a propagation path other than the 1st propagation path is called an undesired wave (U wave), and their power ratio            P      12        ⁢                   ⁢          (      t      )        =                              a          ~                1            ⁢                           ⁢              (        t        )                                      a          ~                2            ⁢                           ⁢              (        t        )            is, in particular, defined as the instantaneous DUR. This instantaneous DUR is the reciprocal in relation to the above-defined instantaneous power ratio P21(t).
Further, in many times, DUR is defined as the ratio of the time-average of the power of the D wave to the time-average of the power of the U wave, and expressed by D/U as a true value or by 10·log10(D/U) as a decibel.
The spread code Wi generates the spread signal exhibiting an intrinsic spectrum distribution, and thus, in the frequency-selective fading environment in which the propagation path itself has the frequency characteristic, the error {tilde over (ψ)}i(t) shown in the equations 19, 20, 22, and 23 appears strongly.
When the known phase value of the pilot channel is 0 and the channel is assigned to the 0th channel, the in-phase component I0′(t) and quadrature component Q0′(t) of the despread signal in the pilot channel are given as follows.I0′(t)≅{tilde over (β)}(t)cos {{tilde over (ψ)}0(t)+{tilde over (ψ)}(t)  (28)Q0′(t)≅{tilde over (β)}(t)sin {{tilde over (ψ)}0(t)+{tilde over (ψ)}(t)  (29)
The phase correction circuit 23i conducts phase correction shown in the following, to output the in-phase component Ii(t) and quadrature component Qi(t) of the correction signal. Namely,Ii(t)=Ii′(t)I0′(t)+Qi′(t)Q0′(t)  (30)Qi(t)=Qi′(t)I0′(t)−Ii′(t)Q0′(t)  (31)
Substituting the equations 22, 23, 28, and 29 expressing respective components of the despread signal into the equations 30 and 31, the correction signal is given as follows.                                                                                           I                  i                                ⁡                                  (                  t                  )                                            =                            ⁢                                                                                                                  β                        ~                                            2                                        ⁡                                          (                      t                      )                                                        ⁢                  cos                  ⁢                                      {                                                                                            θ                          i                                                ⁡                                                  (                                                      t                            -                                                                                          δ                                1                                                            ⁡                                                              (                                t                                )                                                                                                              )                                                                    +                                                                                                    ψ                            ~                                                    i                                                ⁡                                                  (                          t                          )                                                                    +                                                                        ϑ                          ~                                                ⁡                                                  (                          t                          )                                                                                      }                                    ⁢                  cos                  ⁢                                      {                                                                                                                        ψ                            ~                                                    o                                                ⁡                                                  (                          t                          )                                                                    +                                                                        ϑ                          ~                                                ⁡                                                  (                          t                          )                                                                                      }                                                  +                                                                                                      ⁢                                                                                          β                      ~                                        2                                    ⁡                                      (                    t                    )                                                  ⁢                sin                ⁢                                  {                                                                                    θ                        i                                            ⁡                                              (                                                  t                          -                                                                                    δ                              1                                                        ⁡                                                          (                              t                              )                                                                                                      )                                                              +                                                                                            ψ                          ~                                                i                                            ⁡                                              (                        t                        )                                                              +                                                                  ϑ                        ~                                            ⁡                                              (                        t                        )                                                                              }                                ⁢                sin                ⁢                                  {                                                                                                              ψ                          ~                                                o                                            ⁡                                              (                        t                        )                                                              +                                                                  ϑ                        ~                                            ⁡                                              (                        t                        )                                                                              }                                                                                                        =                            ⁢                                                                                          β                      ~                                        2                                    ⁡                                      (                    t                    )                                                  ⁢                cos                ⁢                                  {                                                                                    θ                        i                                            ⁡                                              (                                                  t                          -                                                                                    δ                              1                                                        ⁡                                                          (                              t                              )                                                                                                      )                                                              +                                                                                            ψ                          ~                                                i                                            ⁡                                              (                        t                        )                                                              +                                                                                            ψ                          ~                                                o                                            ⁡                                              (                        t                        )                                                                              }                                                                                        (        32        )                                                                                                      Q                  t                                ⁢                                                                   ⁢                                  (                  t                  )                                            =                            ⁢                                                                    -                                                                  β                        ~                                            2                                                        ⁢                                                                           ⁢                                      (                    t                    )                                    ⁢                                                                           ⁢                  sin                  ⁢                                      {                                                                                            θ                          i                                                ⁢                                                                                                   ⁢                                                  (                                                      t                            -                                                                                          δ                                1                                                            ⁢                                                                                                                           ⁢                                                              (                                t                                )                                                                                                              )                                                                    +                                                                                                    ψ                            ~                                                    i                                                ⁢                                                                                                   ⁢                                                  (                          t                          )                                                                    +                                                                        ϑ                          ~                                                ⁢                                                                                                   ⁢                                                  (                          t                          )                                                                                      }                                    ⁢                                                                           ⁢                  cos                  ⁢                                      {                                                                                                                        ψ                            ~                                                    0                                                ⁢                                                                                                   ⁢                                                  (                          t                          )                                                                    +                                                                        ϑ                          ~                                                ⁢                                                                                                   ⁢                                                  (                          t                          )                                                                                      }                                                  +                                                                                                      ⁢                                                                    β                    ~                                    2                                ⁢                                                                   ⁢                                  (                  t                  )                                ⁢                                                                   ⁢                cos                ⁢                                  {                                                                                    θ                        i                                            ⁢                                                                                           ⁢                                              (                                                  t                          -                                                                                    δ                              1                                                        ⁢                                                                                                                   ⁢                                                          (                              t                              )                                                                                                      )                                                              +                                                                                            ψ                          ~                                                i                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                              +                                                                  ϑ                        ~                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                                              }                                ⁢                                                                   ⁢                sin                ⁢                                  {                                                                                                              ψ                          ~                                                0                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                              +                                                                  ϑ                        ~                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                                              }                                                                                                        =                            ⁢                                                -                                                            β                      ~                                        2                                                  ⁢                                                                   ⁢                                  (                  t                  )                                ⁢                                                                   ⁢                sin                ⁢                                  {                                                                                    θ                        i                                            ⁢                                                                                           ⁢                                              (                                                  t                          -                                                                                    δ                              1                                                        ⁢                                                                                                                   ⁢                                                          (                              t                              )                                                                                                      )                                                              +                                                                                            ψ                          ~                                                i                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                              -                                                                                            ψ                          ~                                                0                                            ⁢                                                                                           ⁢                                              (                        t                        )                                                                              }                                                                                        (        33        )            
Using the in-phase component Ii(t) and quadrature component Qi(t) of the correction signal in the decision circuits 241-24n, the information phase of the channel i is obtained as follows. And, based on the obtained information phase of the channel i, the received symbol, i.e., received information of the channel i is decided in accordance with the rule assigned on the transmission side. The information phase of the channel i is given as follows.                                                                        information                ⁢                                                                   ⁢                                  phase                  i                                ⁢                                                                   ⁢                                  (                  t                  )                                            =                            ⁢                              -                                                      tan                                          -                      1                                                        ⁡                                      [                                                                                            Q                          i                                                ⁢                                                                                                   ⁢                                                  (                          t                          )                                                                                                                      I                          i                                                ⁢                                                                                                   ⁢                                                  (                          t                          )                                                                                      ]                                                                                                                          =                            ⁢                                                tan                                      -                    1                                                  ⁡                                  [                                                            sin                      ⁢                                              {                                                                                                            θ                              i                                                        ⁢                                                                                                                   ⁢                                                          (                                                              t                                -                                                                                                      δ                                    1                                                                    ⁢                                                                                                                                           ⁢                                                                      (                                    t                                    )                                                                                                                              )                                                                                +                                                                                                                    ψ                                ~                                                            i                                                        ⁢                                                                                                                   ⁢                                                          (                              t                              )                                                                                -                                                                                                                    ψ                                ~                                                            0                                                        ⁢                                                                                                                   ⁢                                                          (                              t                              )                                                                                                      }                                                                                    cos                      ⁢                                              {                                                                                                            θ                              i                                                        ⁢                                                                                                                   ⁢                                                          (                                                              t                                -                                                                                                      δ                                    1                                                                    ⁢                                                                                                                                           ⁢                                                                      (                                    t                                    )                                                                                                                              )                                                                                +                                                                                                                    ψ                                ~                                                            i                                                        ⁢                                                                                                                   ⁢                                                          (                              t                              )                                                                                -                                                                                                                    ψ                                ~                                                            0                                                        ⁢                                                                                                                   ⁢                                                          (                              t                              )                                                                                                      }                                                                              ]                                                                                                        =                            ⁢                                                                    θ                    i                                    ⁢                                                                           ⁢                                      (                                          t                      -                                                                        δ                          i                                                ⁢                                                                                                   ⁢                                                  (                          t                          )                                                                                      )                                                  +                                                                            ψ                      ~                                        i                                    ⁢                                                                           ⁢                                      (                    t                    )                                                  -                                                                            ψ                      ~                                        0                                    ⁢                                                                           ⁢                                      (                    t                    )                                                                                                          (        34        )            
In the last right side of the equation 34 expressing the reception information of the channel i, the first term is a true value of the received phase, and the second and subsequent terms indicate disturbances. The Doppler shift error, the fading phase error, and the delay error appearing in the equations 12 and 13 now disappear, thus showing that the phase correction circuits operate effectively. However, it is clear that, as shown by the second and third terms, the frequency-selective fading errors can not be removed, and remain as factors deteriorating the communication quality.
The received information may be decided from the information phase within a single segment shown in the equation 34. However, the received information can be decided from the average value of the information phases in a plurality of segments in the same symbol period, in order to improve the noise immunity and communication quality.
For example, for obtaining the averages of the in-phase component Ii(t) and quadrature component Qi(t) of the correction signal within a symbol, it is noted that the amplitude distortion in a symbol is nearly constant, to obtain the average values using the equations 32 and 33. Then, by deciding the information phase from the obtained average values, the communication quality can be further improved.
Further, the averages may be obtained after removing the amplitude distortions in the equations 32 and 33. Namely, utilizing the fact that the amplitude value of the correction signal is obtained by squaring the sum of the square of the in-phase component and the square of the quadrature component, the amplitude distortion can be easily removed.